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Title: Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling

Abstract

Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol’) indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. In this paper, we propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol’ index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol’ indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol’ indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol’ indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol’ indices converge to the true/deterministic Sobol’ indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then appliedmore » to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.« less

Authors:
 [1];  [2];  [3]
+ Show Author Affiliations
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. Univ. of Tennessee, Knoxville, TN (United States)
  3. Johns Hopkins Univ., Baltimore, MD (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Department of the Navy, Office of Naval Research (ONR)
OSTI Identifier:
1651313
Alternate Identifier(s):
OSTI ID: 2325479
Grant/Contract Number:  
AC05-00OR22725; N00014-16-1-2582; N00014-16-1-2370; ERKJ352
Resource Type:
Accepted Manuscript
Journal Name:
Mechanical Systems and Signal Processing
Additional Journal Information:
Journal Volume: 148; Journal Issue: na; Journal ID: ISSN 0888-3270
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; Global Sensitivity Analysis; Imprecise Probability; Bayesian Multimodel Inference; Importance Sampling; Uncertainty Quantification; Composite Material

Citation Formats

Zhang, Jiaxin, TerMaath, Stephanie, and Shields, Michael D. Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling. United States: N. p., 2020. Web. doi:10.1016/j.ymssp.2020.107162.
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Zhang, Jiaxin, TerMaath, Stephanie, & Shields, Michael D. Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling. United States. https://doi.org/10.1016/j.ymssp.2020.107162
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Zhang, Jiaxin, TerMaath, Stephanie, and Shields, Michael D. Sun . "Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling". United States. https://doi.org/10.1016/j.ymssp.2020.107162. https://www.osti.gov/servlets/purl/1651313.
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@article{osti_1651313,
title = {Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling},
author = {Zhang, Jiaxin and TerMaath, Stephanie and Shields, Michael D.},
abstractNote = {Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol’) indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. In this paper, we propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol’ index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol’ indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol’ indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol’ indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol’ indices converge to the true/deterministic Sobol’ indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then applied to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.},
doi = {10.1016/j.ymssp.2020.107162},
journal = {Mechanical Systems and Signal Processing},
number = na,
volume = 148,
place = {United States},
year = {Sun Aug 09 00:00:00 EDT 2020},
month = {Sun Aug 09 00:00:00 EDT 2020}
}
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